10,889 research outputs found
On the finiteness and stability of certain sets of associated primes ideals of local cohomology modules
Let be a Noetherian local ring, an ideal of and a
finitely generated -module. Let be an integer and
r=\depth_k(I,N) the length of a maximal -sequence in dimension in
defined by M. Brodmann and L. T. Nhan ({Comm. Algebra, 36 (2008), 1527-1536).
For a subset S\subseteq \Spec R we set S_{{\ge}k}={\p\in
S\mid\dim(R/\p){\ge}k}. We first prove in this paper that
\Ass_R(H^j_I(N))_{\ge k} is a finite set for all }. Let
\fN=\oplus_{n\ge 0}N_n be a finitely generated graded \fR-module, where
\fR is a finitely generated standard graded algebra over . Let be
the eventual value of \depth_k(I,N_n). Then our second result says that for
all the sets \bigcup_{j{\le}l}\Ass_R(H^j_I(N_n))_{{\ge}k} are
stable for large .Comment: To appear in Communication in Algebr
Is Vietnam economic paradigm sustainable for catch up
In the course of catching-up, Vietnam faces risks in two sectors: in real sector and in financial sector. In this paper we focus mostly on risk in real sector: the risk of getting stuck in middle-income trap. Vietnam is still far lagged behind her neighbors and much more further to developed economies. Does the economic paradigm that Vietnam follows in the last two decades allow her to catch up with those economies? We show that Vietnam’s economic growth in the last two decades based essentially on cheap but low skill labor and physical capital. Participation in international and regional production network probably lock Vietnam in low-tech position, hence low value added. If Vietnam keeps on growing in present paradigm, hardly can it catch up the neighboring economies.Flying geese paradigm, VAR models, TFP, Technological improvement, catch-up, Vietnam.
On the cofiniteness of generalized local cohomology modules
Let be a commutative Noetherian ring, an ideal of and ,
two finitely generated -modules. The aim of this paper is to investigate the
-cofiniteness of generalized local cohomology modules \displaystyle
H^j_I(M,N)=\dlim\Ext^j_R(M/I^nM,N) of and with respect to . We
first prove that if is a principal ideal then is -cofinite
for all and all . Secondly, let be a non-negative integer such
that \dim\Supp(H^j_I(M,N))\le 1 \text{for all} j Then is
-cofinite for all and \Hom(R/I,H^t_I(M,N)) is finitely generated.
Finally, we show that if or then is
-cofinite for all .Comment: 16 page
- …